Finding Optimal Piano Fingerings (UMAP)

While preparing to perform a piece of music, a pianist must work out a fingering for the piece. Sometimes, the optimal fingering is obvious and emerges naturally during sight-reading. Other times, when the easiest fingering is unclear, the sheet music will show a suggested fingering that was offered by an experienced player. But often, neither of these is the case, and the pianist must try out a variety of different fingerings. The intent of this paper is to present an efficient "dynamic programming" method for finding optimal fingerings.

Table of Contents:

INTRODUCTION

ASSUMPTIONS AND NOTATIONS

SOLVING THE PROGRAM WITH DYNAMIC PROGRAMMING

AN EXAMPLE
Step 1 (Stage 9)
Step 2 (Stage 8)
Step 3 (Stage 7)
Step 4 (Stage 6)
Step 5 (Stage 5)
Step 6 (Stage 4)
Step 7 (Stage 3)
Step 8 (Stage 2)
Step 9 (Stage 1)

COMMENTS

REFERENCES

ABOUT THE AUTHORS